Two-Level System Dynamics in the Long-Time Limit: A Power-Law Time Dependence

1996 ◽  
Vol 76 (12) ◽  
pp. 2085-2088 ◽  
Author(s):  
H. Maier ◽  
B. M. Kharlamov ◽  
D. Haarer
Keyword(s):  
System Dynamics ◽  
Time Dependence ◽  
Power Law ◽  
Time Limit ◽  
Level System ◽  
Long Time

Double Power Law in the Japanese Financial Market

2019 ◽  
Vol 7 (1) ◽  
pp. 28-35
Author(s):  
Sudhir Jain ◽  
Takuya Yamano
Keyword(s):  
Time Dependence ◽  
Financial Market ◽  
Power Law ◽  
Power Laws ◽  
Recent Analysis ◽  
Short Term ◽  
Power Law Decay ◽  
Long Time ◽  
Ising Spins

The authors study the persistence phenomenon in the Japanese stock market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data from the Japanese financial market. By studying the time dependence of the spins, they find clear evidence for a double-power law decay of the proportion of shares that remain either above or below ‘starting' values chosen at random. The results are consistent with a recent analysis of the data from the London FTSE100 market. The slopes of the power-laws are also in agreement. The authors estimate a long time persistence exponent for the underlying Japanese financial market to be 0.5. Furthermore, they argue that the presence of a double power law in the decay of the persistence probability could be the signature of the presence of both speculative (short-term) and long-term traders in the market.

scholarly journals A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Unit Circle ◽  
Stationary State ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Limit ◽  
The Other ◽  
Unitary Matrix ◽  
Initial State ◽  
Time Quantum ◽  
Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion

2013 ◽  
Vol 20 (01) ◽  
pp. 1350002 ◽  
Author(s):  
F. Giraldi ◽  
F. Petruccione
Keyword(s):  
Time Evolution ◽  
Power Law ◽  
Weak Coupling ◽  
Inverse Power ◽  
Strong Coupling Regime ◽  
Weak Coupling Regime ◽  
Spectral Densities ◽  
Inverse Power Law ◽  
Critical Configurations ◽  
Long Time

The exact dynamics of a quantum damped harmonic oscillator coupled to a reservoir of boson modes has been formally described in terms of the coupling function, both in weak and strong coupling regime. In this scenario, we provide a further description of the exact dynamics through integral transforms. We focus on a special class of spectral densities, sub-ohmic at low frequencies, and including integrable divergencies referred to as photonic band gaps. The Drude form of the spectral densities is recovered as upper limit. Starting from special distributions of coherent states as external reservoir, the exact time evolution, described through Fox H-functions, shows long time inverse power law decays, departing from the exponential-like relaxations obtained for the Drude model. Different from the weak coupling regime, in the sub-ohmic condition, undamped oscillations plus inverse power law relaxations appear in the long time evolution of the observables position and momentum. Under the same condition, the number of excitations shows trapping of the population of the excited levels and oscillations enveloped in inverse power law relaxations. Similarly to the weak coupling regime, critical configurations give arbitrarily slow relaxations useful for the control of the dynamics. If compared to the value obtained in weak coupling condition, for strong couplings the critical frequency is enhanced by a factor 4.

scholarly journals STABILITY ANALYSIS OF CELLULAR AUTOMATA GENERATED CLUSTERS

2005 ◽  
Vol 12 (1) ◽  
pp. 83-90
Author(s):  
R. Šiugždaite
Keyword(s):  
Cellular Automata ◽  
Power Law ◽  
State Parameter ◽  
Urban System ◽  
Complex Behaviour ◽  
Cellular Automata Model ◽  
Self Organized ◽  
Tai Ji ◽  
Long Time ◽  
Ca Model

The development of regional urban system still remains one of the main problems during the human race history. There are a lot of problems inside this system like overcrowded cities and decaying countryside. All these situations can be reproduced by modelling them using Cellular Automata (CA) [1, 2, 5]. CA models implement algorithms with simple rules and parameter controls, but the result can be a complex behaviour. A stability of naturally formed self‐organized urban system depends on its critical state parameter τ in the power law log(f(x)) = ‐τlog(x). If the system reaches self‐organized critical (SOC) state then it remains in it for a long time. The CA model URBACAM (URBAnistic Cellular Automata Model) describes the long‐lasting term behaviour and shows that the change in behaviour is sensitive to the urban parameter τ of the power law. Regionines urbanistines sistemos vystymasis išlieka viena iš opiausiu problemu žmonijos istorijoje. Keletas tokiu uždaviniu kaip miestu perpildymas, nykstančios kaimo vietoves ir t.t. gali būti nesunkiai modeliuojami naudojant lasteliu automatus (LA). LA metodas ypatingas tuo, kad realizuoja algoritma paprastu taisykliu bei parametru valdymo pagalba, tačiau rezultate galima gauti sudetinga elgsena. Natūraliai susiformavusiu urbanistiniu sistemu stabilumas priklauso nuo sistemos krizines savirangos būsenos (KSB) parametro τ. Jei sistema pasiekia KSB, tai ji ilga laika išlieka joje. LA modelis URBACAM charakterizuoja ilgalaike elgsena ir parodo, jog modelyje jos kitimus itakoja eksponentinio desnio urbanistinis parametras τ.

scholarly journals Temporal variations in rockfall and rock-wall retreat rates in a deglaciated valley over the past 11 k.y.

Geology ◽  
2020 ◽  
Vol 48 (6) ◽  
pp. 594-598 ◽  
Author(s):  
Solmaz Mohadjer ◽  
Todd A. Ehlers ◽  
Matthias Nettesheim ◽  
Marco B. Ott ◽  
Christoph Glotzbach ◽  
...  
Keyword(s):  
Power Law ◽  
Time Scale ◽  
Temporal Variations ◽  
Climatic Conditions ◽  
Short Time Scale ◽  
Similar Frequency ◽  
Rock Wall ◽  
Significant Difference ◽  
Long Time ◽  
Frequency Magnitude

Abstract This study addresses the temporal variations in rockfall activity in the 5.2 km2 calcareous cliffs of the deglaciated Lauterbrunnen Valley, Switzerland. We did this using 19 campaigns of repeated terrestrial laser scans (TLS) over 5.2 yr, power-law predicted behavior from extrapolation of the TLS-derived frequency-magnitude relationship, and estimates of long-time-scale (∼11 k.y.) activity based on the volume of preserved postglacial rockfall talus. Results from the short-time-scale observations indicate no statistically significant difference between TLS observations averaging over 1.5 versus 5.2 yr. Rock-wall retreat rates in both cases are 0.03–0.08 mm/yr. In contrast, the power-law predicted rock-wall retreat rates are 0.14–0.22 mm/yr, and long-term rates from talus volumes are 0.27–0.38 mm/yr. These results suggest (1) short (1.5 yr) TLS inventories of rockfalls provide (within uncertainties) similar frequency-magnitude relationships as longer (5.2 yr) inventories, thereby suggesting short observation periods may be sufficient for hazard characterization from TLS, and (2) higher rock-wall retreat rates over long time scales (Holocene averaged) may reflect debuttressing and stress relaxation effects after glacial retreat, and/or enhanced rockfall activity under periglacial (climatic) conditions.

scholarly journals Cancellation of vacuum diagrams and the long-time limit in out-of-equilibrium diagrammatic quantum Monte Carlo

2019 ◽  
Vol 100 (8) ◽  
Author(s):  
Alice Moutenet ◽  
Priyanka Seth ◽  
Michel Ferrero ◽  
Olivier Parcollet
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Time Limit ◽  
Long Time

Turn-on and Charge Build-up Dynamics in Polymer Field Effect Transistors

2005 ◽  
Vol 871 ◽  
Author(s):  
Yohai Roichman ◽  
Nir Tessler
Keyword(s):  
Power Law ◽  
Field Effect ◽  
Field Effect Transistors ◽  
Time Range ◽  
Gate Bias ◽  
Current Dependence ◽  
Turn On ◽  
Long Time ◽  
Source Current ◽  
Short Time

AbstractTurn-on dynamics of polymer field effect transistors were examined experimentally over a wide timescale. We found that the source current dependence on time following switch on of the gate bias exhibits a power law at the short time range, and an exponential decay at the intermediate to long time range. We demonstrate that the transistor dynamic behavior is governed by the channel charge build-up, and can be described accurately by a simple capacitor-resistor distributed line model.

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